1. Field of the Invention
The present invention relates to a method and a device for determining composition amounts of a functional mixture, and particularly to a method and a device for determining the composition amounts of the functional mixture, which can determine composition amounts of a functional mixture composed of N components without actual preparation of the functional mixture.
2. Description of the Related Art
The following various methods have been known hitherto as methods of determining the composition amounts of a functional mixture composed of N components, in terms of composition ratios.
According to a general method, a functional mixture is actually prepared, and it is estimated for the functional mixture by some method whether or not desired functionality has been imparted to the functional mixture.
This method will be described below as it is applied to an emulsion-dispersed material, which is a kind of functional mixture.
The emulsion-dispersed material contains hydrophobic material dispersed in the form of minute oil-in-water droplets in a dispersion medium, and such is used in various fields such as photosensitive materials for photography, cosmetics, foods, chemicals, etc.
As one of the functions required of the emulsion-disperses material, it is required that the size of the minute oil-in-water droplets is prevented from increasing to a fixed value or more with the passing of time and that no over-size oil droplets are generated. The necessity of this function is disclosed in, for example, Japanese Patent Application Laid-Open (JP-A) No. 9-131519, and this publication discloses a method of estimating the functionality of the emulsion-dispersed material by directly observing over-size oil droplets. Further, JP-A No. 10-260488 discloses a method of directly estimating the number of over-size oil droplets.
Furthermore, as an example where the functionality necessary for the emulsion-dispersed material is hindered, Japanese Patent Application Publication (JP-B) No. 60-53865 discloses an observation example of deposition of a coupler (the hydrophobic material) which would have been originally dissolved in the minute oil droplets.
In order to prepare the emulsion-dispersed material such that occurrence of over-size oil droplets and deposition are prevented, it is required that the emulsion-dispersed material is actually prepared and such estimations as are carried out in the above prior art examples are carried out on the actually prepared emulsion-dispersed material to check the functionality of the emulsion-dispersed material.
Beside the above, JP-A No. 2000-89404 discloses a method of specifying solubility parameters of a hydrophobic material and a high boiling point solvent, and thus volume percentages of the hydrophobic material and the solvent that will prevent deposition of the hydrophobic material. According to this method, an emulsion-dispersed material composition which can suppress deposition can be achieved in advance.
However, in the case where many kinds of hydrophobic materials are added or the like, satisfactory prediction cannot be performed.
Further, the composition of an emulsion-dispersed material which does not deposit can be determined before preparation thereof, by applying a method for preventing the deposition of the hydrophobic material to the emulsion-dispersed material. However, it is difficult to pre-empt the occurrence of over-size oil droplets.
Beside these, JP-A No. 2000-171956 (a corresponding patent : U.S. Pat. No. 6,117,601) discloses a method of judging a treatment liquid (a kind of functional mixture) and treatment conditions for a silver halide photosensitive material, and a correction method therefor.
JP-A No. 2000-171956 discloses a method of determining a Mahalanobis distance from a group of many normal states (as expected of a functional mixture provided with functionality) to thereby judge a treatment liquid for which it is unclear whether the liquid is normal or not (i.e., it is unclear whether the liquid will have the required functionality). Further, it is disclosed that for each constituent component, the Mahalanobis distance is compared between a case where all the constituent components are contained and cases where each component is excluded, thereby detecting any constituent components that cause xe2x80x9cnon-normalityxe2x80x9d.
By the above method, the constituent components to be corrected can be specified. However, a method of determining how the constituent components should be corrected must be additionally considered.
If necessary, tests and estimations must be newly carried out, and there are cases where a correction value cannot be quickly predicted.
An object of the present invention is to provide a method and a device by which the composition amounts of each of constituent components effecting functionality of a functional mixture, such as an emulsion-dispersed material or the like, are brought closer to correlation coefficients between respective constituent components of functional mixtures which have been previously achieved, before the functional mixture is actually prepared, and accordingly determining the composition amounts of the constituent components and imparting the functionality.
In order to attain the above object, according to the present invention, there is provided a functional mixture composition amount determining method for determining a composition amount of each of N constituent components when a functional mixture including the N constituent components is to be prepared, the method including the steps of: (1) determining a correlation matrix R having as elements correlation coefficients between composition amounts c1, c2, c3, . . . , cN of the N constituent components of each of M functional mixtures C, each functional mixture C being known in advance to have required functionality, and M being greater than N; (2) calculating a Mahalanobis distance D2 or D for all of composition amounts u1, u2, u3, . . . , uN of the N constituent components of a functional mixture U, it being unknown whether or not the functional mixture U has the required functionality; and (3) varying the composition amount of at least one of the constituent components of the functional mixture U such that the Mahalanobis distance is reduced, and determining as a composition amount of the at least one constituent component in the functional mixture to be prepared the composition amount at which the Mahalanobis distance is reduced.
xe2x80x83D2=URxe2x88x921UT xe2x80x83xe2x80x83(1)
UT represents the transposed matrix of a matrix U, the matrix U is (u1, u2 u3, . . . , uN), and each composition amount ck of each of the M functional mixtures C and each composition amount uk of the functional mixture U is transformed such that, for each of the N constituent components, the average of the composition amounts of the constituent component in the M functional mixtures C and the functional mixture U is 0 and the standard deviation of the composition amounts thereof is 1.0.
Further, in order to attain the above object, according to the present invention, there is provided a functional mixture composition amount determining device for determining a composition amount of each of N constituent components when a functional mixture including the N constituent components is to be prepared, the device including: a storage component which stores at least one of a correlation matrix R having as elements the correlation coefficients between composition amounts c1, c2, c3, . . . , cN of the N constituent components of each of M functional mixtures C and the inverse matrix of the correlation matrix R, each functional mixture C being known in advance to have required functionality, and M being greater than N; a calculation component which calculates a Mahalanobis distance D2 or D for all of composition amounts u1, u2, u3, . . . , uN of the N constituent components of a functional mixture U, it being unknown whether or not the functional mixture U has the required functionality; and a determining component which varies the composition amount of at least one of the constituent components of the functional mixture U such that the Mahalanobis distance is reduced, and determining as a composition amount of the at least one constituent component in the functional mixture to be prepared the composition amount at which the Mahalanobis distance is reduced.
In the above invention, one in turn of each of the constituent components of the functional mixture U is excluded from the functional mixture U to achieve N sets of (N-1) composition amounts. By using the N sets of (N-1) composition amounts of remaining constituent components (i.e., the remaining constituent components achieved by excluding the one constituent component from the constituent components), the Mahalanobis distance is successively calculated for each of the N sets of (N-1) composition amounts. Thereafter, a difference between the Mahalanobis distance calculated by using the N composition amounts and the Mahalanobis distance calculated by using the (N-1) composition amounts is calculated for each set. By varying the composition amount of the constituent component whose exclusion produces the largest difference or by successively varying the composition amount of a predetermined number of the constituent components, from the constituent component whose exclusion produces the largest difference to the excluded constituent component that is the predetermined number of places down the order if the constituent components are sorted in descending order of size of the difference, composition amounts in cases where the Mahalanobis distance for the N composition amounts containing the thus varied composition amount is consequently reduced can be determined (selected) as the composition amounts of the functional mixture.
A new correlation matrix may be calculated by appending to the matrix of composition amounts of the functional mixtures C, which are previously known to have the necessary functionality, the composition amounts of the functional mixture U, which now has the functionality due to determination of the composition amounts, and this correlation matrix may then be used as the correlation matrix R.
The composition amounts can be more accurately determined if the method in which the Mahalanobis distance is reduced is replaced by a method in which the Mahalanobis distance is minimized.
In the step (1) of the present invention, M functional mixtures C which have been previously judged to have necessary functions by some method are collected, and all the correlation coefficients among N composition amounts c1, c2, c3 . . . , CN of N types of constituent components (M greater than N) are calculated so as to determine the correlation matrix R having the correlation coefficients as elements.
xe2x80x9cFunctional mixturexe2x80x9d in the present invention includes all mixtures that contain two or more kinds of constituent components and have a xe2x80x9cfunctionxe2x80x9d.
Here, xe2x80x9cfunctionxe2x80x9d is a xe2x80x9crequirementxe2x80x9d for use of the mixture, and does not mean a function in the narrow sense of a positive action being required. xe2x80x9cRequirementxe2x80x9d includes functions in a broader sense; for example, that the mixture has no side reaction, that deterioration of the mixture is low, and the like may be referred to as functions in the present invention.
When there are two or more xe2x80x9crequirementsxe2x80x9d, the functions to be provided by the present invention may be all of these requirements or just some of the requirements.
An xe2x80x9cemulsion-dispersed material for photosensitive materials for photographyxe2x80x9d is included in xe2x80x9cfunctional mixturesxe2x80x9d of the present invention, and the term xe2x80x9cfunctional mixturexe2x80x9d will be described in more detail by exemplifying an emulsion-dispersed material for photosensitive materials for photography.
The constituent components of an emulsion-dispersed material for a photosensitive material for photography are a functional mixture containing water, gelatin, a coupler and oil as constituent components. Requirements of the emulsion-dispersed material for a photosensitive material for photography include, for example, that oil-soluble materials such as coupler, oil, etc. are provided in the form of oil droplets in the photosensitive material and show a coloring reaction, and that neither an increase in size of the minute oil droplets nor deposition of the coupler occurs. The former is a xe2x80x9cfunctionxe2x80x9d in the narrow sense, and the latter is a xe2x80x9crequirementxe2x80x9d that the emulsion-dispersed material shows no side reaction, and both are considered xe2x80x9cfunctionsxe2x80x9d in the present invention.
The xe2x80x9cfunctional mixturexe2x80x9d in the present invention may be a liquid material such as a solid fine-particle dispersed material of an emulsified material, a solution, a pigment, etc., or a solid material such as an alloy, a polymer or the like, or a powdery mixture comprising a number of components.
The present invention is particularly effective in cases where much time and cost might be needed to estimate functionality and cases where there is no objective quantitative method for estimation of functionality (for example, the scent of a perfume, the taste of a drink, etc.).
In the present invention, the N kinds of constituent components of the functional mixture may correspond to all constituent components of the mixture or just some of the constituent components. In other words, the present invention may be applied to all of the constituent components or just some of the constituent components (but at least two of the constituent components).
The number (N) of the kinds of constituent components to be used must be at least two, and the upper limit of the number is restricted as follows. That is, when N constituent components are used, it is required that the number M of functional mixtures which are already known to have the necessary functions is larger than the number N. Preferably, M is at least twice N, and more preferably M is at least five times N.
Another restriction resides in the increase of calculation time due to increases of the numbers N and M. The calculation time is dependent on advances in the performance of computers and the like, and thus a preferable upper limit number is not necessarily determined in relation to N and M. However, the numbers N and M must be determined in consideration of the fact that as the numbers N and M increase, the calculation time is also increased. In consideration of calculations of correlation coefficients, it is preferable that M is equal to 20 or more irrespective of N.
The xe2x80x9ccorrelation matrixxe2x80x9d in the present invention is the same as generally known correlation matrices, and is achieved by calculating respective correlation coefficients of the respective constituent components and arranging the correlation coefficients as shown in the following equation (2).                     (                                                            r                11                                                                    r                12                                                                    r                13                                                    Λ                                                      r                                  1                  ⁢                  N                                                                                                        r                21                                                                    r                22                                                                    r                23                                                    Λ                                                      r                                  2                  ⁢                  N                                                                                        M                                      M                                      M                                                      xe2x80x83                                                    M                                                                          r                N1                                                                    r                N2                                                                    r                N3                                                    Λ                                                      r                NN                                                    )                            (        2        )            
For example, an element r12 in the equation (2) represents the correlation coefficient between the constituent components c1 and c2, and r21 represents the correlation coefficient between the constituent components c2 and c1. Of course, r12=r21. rNN represents the correlation coefficient between the constituent components cN and cN (the same constituent component), and thus is always equal to 1. Accordingly, the correlation matrix is a matrix which has all diagonal elements being 1 and is symmetrical with respect to the diagonal. This correlation matrix R, or an inverse matrix thereof, is stored in a storage component.
In the step (2) (or the calculation component), the Mahalanobis distance represented by the equation (1) is calculated for each of the N composition amounts u1, u2, u3, . . . , uN of the N constituent components of the functional mixture U in which it is unclear whether a function will be present or not. The Mahalanobis distance may be defined by D2 or by the square root of D2 (i.e., D).
In the step (3) (or the determining component), the composition amount of at least one of the constituent components of the functional mixture U is varied such that the Mahalanobis distance (D or D2) is reduced, and a composition amount for which the Mahalanobis distance is reduced is determined as the composition amount of the functional mixture.
Specifically, for example, the composition amount of a certain constituent component is increased or reduced, and then calculation of the Mahalanobis distance is carried out again. At this time, if the thus-calculated Mahalanobis distance is smaller than the initially calculated Mahalanobis distance, the composition amount of the constituent component concerned will be determined as the composition amount of the functional mixture.
Here, it may be unnecessary to vary the composition amount such that the Mahalanobis distance becomes a minimum value. As long as the Mahalanobis distance is smaller than the initially calculated Mahalanobis distance, the composition value at this time may be adopted. However, from the viewpoint of accuracy, it is preferable if a composition amount that produces a minimum value is determined as the composition amount of the functional mixture.
Next, a preferable operation in step (3) (or the determining component) will be described. By using the remaining (N-1) constituent components when only one constituent component is omitted from the N constituent components of the functional mixture U, the Mahalanobis distance is calculated for each set of (N-1) composition amounts. That is, in the creation of the correlation matrix R and the calculation of the Mahalanobis distance, the same calculation as in the step (2) (or the calculation component) is carried out except that every k-th constituent component (with k ranging from 1 to N) is excluded by turn from the functional mixture, until one-by-one exclusion of each of the N constituent components is completed, and Mahalanobis distances Dk (or Dk2) (i.e., each Mahalanobis distance when the k-th constituent component is excluded) is calculated (k is integers from 1 to N). This calculation is completely the same as the calculation of the Mahalanobis distance in the step (3) (or the determining component) However, the correlation matrix R used for calculating the Mahalanobis distance Dk (or Dk2) for each set of the (N-1) composition amounts is an (N-1xc3x97N-1) matrix because one composition amount is excluded.
The more the Mahalanobis distance resulting when a k-th constituent component is excluded is smaller than the initial Mahalanobis distance calculated in the step (3) (or the determining component), that is, the larger the difference between the Mahalanobis distance for the N composition amounts and the Mahalanobis distance for the (N-1) composition amounts, the more the Mahalanobis distance will be reduced by varying the composition amount of the k-th constituent component (the excluded constituent component) in the functional mixture U.
Therefore, differences xcex94Dk (=D-Dk or D2-Dk2) between the Mahalanobis distance calculated for the N constituent components and the Mahalanobis distance calculated for each set of the (N-1) constituent components are calculated, and the differences thus calculated for the respective sets of the (N-1) constituent components are arranged in decreasing order (here, the number of the sets is equal to N). In the decreasing order of the differences, the composition amount of each k-th constituent component (k being from 1 to N) is varied to reduce the Mahalanobis distance. That is, the composition amount of the constituent component that produces the largest difference when excluded is varied, or each of the composition amounts of constituent components from the constituent component corresponding to the largest difference to a constituent component a predetermined number of places down the decreasing order is successively varied. Then composition amounts for which the Mahalanobis distance for the N composition amounts including the varied composition amount is reduced are determined as the composition amounts of the functional mixture.
However, instead of obtaining N Mahalanobis distances, one for each case of excluding the k-th constituent component (k being from 1 to N), comparing these Mahalanobis distances and then sorting by the sizes of the differences, it is also possible to use orthogonal arrays. The first level in a k-th column thereof is defined by calculation with the k-th constituent component, and the second level is defined by calculation without the k-th constituent component. Rankings of respective differences may then be obtained.
The main advantage of using orthogonal arrays is an increase in calculation accuracy. For each level of the constituent components allocated to the respective columns of the orthogonal arrays, at least two data repetitions (two in the case of an L4 orthogonal arrays) are input, and the average thereof is calculated to be the distance. Thus, a higher accuracy than in a case where the number of levels is 1 can be expected. As the orthogonal table becomes larger, the number of data repetitions increases correspondingly.
Further, the constituent components do not necessarily all affect the Mahalanobis distance independently. It is conceivable that the constituent components are mutually influential. However, by using orthogonal arrays, the effects of each component can be extracted.
After the composition amounts of the functional mixture U, to which functionality has been given by the determination of the composition amounts, are appended to the composition amounts of the functional mixtures C, which have been previously known to have the necessary function, a new correlation matrix may be calculated and used as the correlation matrix R as described above. With these calculations, the correlation matrix is continuously renewed, and thus more accurate composition amounts can be determined.